Experimental physics has long been exploring different ways of containing charged or neutral particles in an isolated space, either for precision measurements of the fundamental constants or for monitoring their interactions. As is well known, the theoretical description of atoms or elementary particles is in the domain of quantum mechanics. In the late 1930s, out of molecular-bee physics, mass spectrometry and particle physics grew the idea of building a trap to suspend charged particles without a material wall. A more systematic study began in the early 1950s, focusing on the use of a multipole electric field for "trapping" and storing particles for a prolonged period of time.
There are two major types of traps which have been used to trap ions for the purpose of conducting precision measurements. The first type is the Paul trap, often identified as the RF trap (W. Paul, Rev. Mod. Phys. 62, 531, 1990). It uses hyperbolic electrodes in a vacuum apparatus. These electrodes, symmetric about a vertical axis, consist of one ring electrode and two endcap electrodes and all three electrodes are of hyperboloid geometry (see FIG. 1). An alternating voltage of a certain frequency is applied between the endcap and the ring electrodes. An ion injected into the space defined by these electrodes is therefore subject to an RF electric field such that its cyclic motion in response to the alternating voltage, i.e., micromotion, is 180 degrees out of phase with respect to the electric force. Because the electric field is inhomogeneous, the force averaged over one period of one micromotion is in the direction of the weaker field amplitude, i.e., toward the center of the trap, independent of the sign of the charge. Thus, a "pseudo-potential well" is generated to confine the ion.
The second type of ion trap is the Penning trap which uses the same electrode configuration as the Paul trap. Instead of an RF voltage as used in the Paul trap, a static potential is applied between the ring and the endcaps which generates a static potential well in the vertical axis. Meanwhile, a repulsive potential in the horizontal plane is generated which is then overcome by superimposing a static magnetic field along the vertical axis. The horizontal motion of the trapped ions is a composite of circular cyclotron orbits primarily due to the magnetic field and a circular drift magnetron motion in response to the cross product of the electric field and the magnetic field vectors, i.e., E.times.B about the vertical axis. The ion is thus confined in the space defined by the hyperbolic ring electrodes and the two endcaps.
Both the Paul and Penning traps can provide long term confinement of charged particles. It is not uncommon to store ions in the trap for days. There are several advantages arising from the long term storage when the ion trap is used for spectroscopy. The first advantage is the reduction of the minimum energy uncertainty in the frequency measurements as the result of "transit time broadening". The longer the ion is trapped, the less is the uncertainty in the energy measurement due to Heisenberg's uncertainty principle. A second advantage is the more accurate frequency measurement because of the reduction in Doppler shifts. As the trapping time increases, the average velocity of the trapped ion asymptotically approaches zero. According to the Lamb-Dicke's theory, when the dimension of the confinement is sufficiently small, the long duration of confinement can make the first-order Doppler frequency shift negligible. Furthermore, a laser cooling technique was developed by Dehmelt and Wineland in 1975 (Phys. Rev. Let. 41, 233, 1978), and also by Haensch and Schawlow (Opt. Comm. 13, 68, 1975) by which the trapped ions can be "cooled" to very low energies close to absolute zero temperature whereby the second-order Doppler shifts are reduced. A very high degree of accuracy in frequency measurement for the trapped ions can therefore be achieved. The confinement of ions at low energy in an isolated and unperturbed condition for a long duration allows one to make more precise clocks and to perform various kinds of extremely sensitive atomic and nuclear measurements.
One important application of ion traps is in improving the performance of atomic clocks or frequency standards. Atomic clocks play an indispensable role in modern electronic technology and also have important applications in pure research. The principle of an atomic clock is to servo control a conventional frequency standard, for example, a quartz crystal oscillator, so that its frequency resonates with an atomic energy level splitting which, according to the principles of quantum mechanics, is immutable and the same for all atoms. Current devices measure the energy level splitting of cesium atoms in an atomic beam. The accuracy of the cesium clock is however limited because the cesium atoms in the atomic clock move at a speed of several hundred meters per second through the apparatus. These moving atoms have a distribution of velocities which broadens and shifts the atomic resonance due to the Doppler effect. An additional source of broadening is caused by "transit time broadening". It occurs because the atoms spend no more than a few milliseconds in the measuring apparatus. Due to these effects, the accuracy of commercial atomic clocks is limited to about 10.sup.-11 while laboratory devices can reach 10.sup. -14.
Trapped ion atomic clocks are in principle more accurate than atomic beam clocks because the atoms are essentially stationary. Since the observation time can be indefinitely long, transit time broadening is eliminated. Doppler shifts similarly can average to zero so that clock accuracies can be improved by several orders of magnitude to the 10.sup.-15 to 10.sup.-18 range. This improved accuracy is immediately useful in communications and navigation.
Trapped ion clocks, both with and without laser cooling, have already been constructed by several groups. (see L. S. Cutler et. al. Appl. Phys B39, 251 1986), and J. J. Bollinger et. al. Phys. Rev. Letters 54, 1000 1985). FIG. 2 shows an atomic .energy level diagram utilized in a laser-cooled clock as initially proposed and demonstrated by Dehmelt (see IEEE Trans. on Inst. & Meas. 1M-31, p. 83, (1982). As shown in FIG. 2, the three atomic energy levels form two coupled energy transition systems, i.e., a "cooling transition" between levels 1 and 2, and a "clock transition" between levels 1 and 3. The ion is chosen so that the clock transition, i.e., the energy shift between energy levels 1 and 3, is extremely narrow and insensitive to environmental perturbations. It determines the stability and accuracy of the clock. The cooling transition, on the other hand, is used to detect the state of the clock transition and also can be used for laser cooling the atom. It has only an indirect effect on the accuracy of the clock.
A block diagram of a typical laser-cooled clock is shown in FIG. 3. Laser beam 6 drives the cooling transition and microwave source 8 drives the clock transition. As shown in FIG. 3, the confined ion 10 is irradiated with laser beam 6, which is selected and controlled to have a frequency corresponding to the energy shift between energy levels 1 and 2. In absorbing laser beam photons 6, confined ion 10 is pumped to level 2, causing a spontaneous emission of scattered photons 12 which are detected by photodetector 14. When microwave source 8 resonates with the clock transition between levels 1 and 3, it drives confined ion 10 to energy level 3 in FIG. 2. At energy level 3, confined ion 10 is not absorbed by laser beam 6, thereby maintaining its energy level at level 3, which in turn reduces scattered photons 12 emitted by the cooling transition between energy levels 1 and 2. Thus, the three-level system acts as a quantum amplifier where the resonance in the weak clock transition produces a large change in the light scattered from the strong cooling transition. This signal is detected by photo-detector 14 and used to control a servo loop which locks microwave source 8 to the atomic clock frequency. The output of the device is then the microwave signal servo locked to the atomic clock transition. Note that although a microwave clock transition is shown in FIG. 2, the system also works equally well with an optical clock transition.
Several limitations on the performance of the Paul trap and the Penning trap have become apparent in recent years. The three-dimensional hyperbolic metallic electrodes for accurate generation of the quadrupole electric field are difficult to machine for large-scale manufacturing. Beatty showed in 1978 (Phys. Rev. A33, 3645, 1986) how the hyperboloids of revolution could be replaced by conical electrodes and still retain a field which remained quadrupole up to the eighth order. However, the conical electrodes are still difficult to fabricate. The Penning trap has another limitation because of the use of crossed electrostatic and magnetic fields. The requirement of a magnetic field not only places a burden on the space utilization near the ion trap and the complexity of the electric circuitry, but also the magnetic field is difficult and expensive to generate. It is for these reasons that broader applications of ion trap technology in the scientific and engineering communities have been severely restricted.
A second contributing limitation of the prior art is the inability to manufacture small traps. It is well known in the art that the field strength of a trap is inversely related to its trap size. Trap performance thus depends on the ability to machine complex parts no larger than a few thousandths of an inch in dimension. Mass fabrication is not feasible with the hyperboloid electrodes required by both the Paul and Penning traps.
Another limitation faced by the prior art is the breakdown voltage of the trap. This limits the strength of the trap potential and indirectly the trap size. It is well known that conventional machined electrodes break down at voltages which are factors of 10 to 1000 lower than that which was predicted by the Fowler-Nordheim theory of quantum mechanics (Germian and Rohrbach, Vacuum 18, 371, 1967). This is because machined electrodes inevitably contain a few small protrusions on the order of 1 micron in size which enhance the electric field by factors of 10 to 1000 and initiate the breakdown. Traps made by photolithographic or semiconductor techniques, however, should have breakdown voltages several orders of magnitude higher than those made with machined electrodes. This is because photolithographic electrodes are smooth on the micron scale and obey the Fowler-Nordheim law. Consequently, they should withstand electric fields of about 10.sup.6 volts/cm rather than 10.sup.4 volts/cm which is customary for conventional trap designs. Since the trapping potential is proportional to the square of the applied voltage, photolithographic traps can be far stronger or smaller than conventional traps. However, photolithography is most successful when used to make planar structures; conical or cylindrical shapes can be made only with great difficulty. Hence, planar traps are a natural choice for photolithography.
Another limitation of the prior art is a quantum limit on single-atom clock performance as pointed out by Wineland in 1981 (Wineland et. al., Phys. Rev. A36, 2220, 1987) that for optimum performance of the atomic clock, many separate single-atom clocks should be operated simultaneously. However, the difficulty of constructing such micro clocks has made the practicality of this approach questionable.